Solid electron wavefunction localization vs delocalization

[dzyaloshinskii]

In a solid, is electron's wavefunciton confined to a molecular orbital between atoms or is it delocalized and extends over the volume?

According to valence bond theory, electrons are localized in bonds between atoms.

But according to band theory (or Bloch wavefunctions), electrons are delocalized.

If it depends on material, then does it make sense to draw a band diagram for a solid whose electrons are localized to bonds (e.g. carbon diamond)?

 

[DrDu]

At least for an insulator, the description of the wave function in terms of delocalized Bloch functions and localized Wannier functions are completely equivalent: https://en.wikipedia.org/wiki/Wannier_function